Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1999 | 19 | 1-2 | 45-65

## On the solution set of the nonconvex sweeping process

EN

### Abstrakty

EN
We prove that the solutions of a sweeping process make up an $R_δ$-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

EN

45-65

wydano
1999
otrzymano
1999-06-05

### Twórcy

autor
• Dipartimento di Matematica Pura e Applicata, Universita di Modena, via Campi 213/B, 41100 Modena, Italy

### Bibliografia

• [1] R.A. Adams, Sobolev Spaces, Academic Press 1975.
• [2] J. Andres, G. Gabor and L. Górniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc., to appear.
• [3] J. Andres, G. Gabor and L. Górniewicz, Topological structure of solution sets to multivalued asymptotic problems, Palacky University (1999), preprint.
• [4] J. Andres, On the multivalued Poincaré operators, Topol. Meth. Nonlin. Anal. 10 (1997), 171-182.
• [5] J. P. Aubin and A. Cellina, Differential Inclusions; Set-valued Maps and Viability Theory, Springer Verlag, Berlin 1984.
• [6] H. Benabdellah, Existence of solutions to the nonconvex sweeping process, preprint, University of Marrakesh, Morocco.
• [7] H. Benabdellah, C. Castaing, A. Salvadori and A. Syam, Nonconvex sweeping process, Journal of Applied Analysis 2 (2) (1996), 217-240.
• [8] D. Bothe, Multivalued Differential Equations on Graphs, Nonlinear Analysis 18 (3) (1992), 245-252.
• [9] C. Castaing and M.D.P. Monteiro Marques, Sweeping process by nonconvex moving sets with perturbation, C.R. Acad. Sci. Paris, Série I 319 (1994), 127-132.
• [10] C. Castaing and M.D.P. Monteiro Marques, Periodic solutions of evolution problem associated with moving convex set, C.R. Acad. Sci. Paris, Série I 321 (5) (1995), 531-536.
• [11] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience Publication, John Wiley & Sons 1983.
• [12] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory, Springer Verlag, New York-Berlin-Heidelberg 1998.
• [13] G. Colombo and V. Goncharov, The Sweeping Process without convexity, preprint, University of Padova, Italy.
• [14] F.S. De Blasi and J. Myjak, On the solution sets for differential inclusions, Bull. Polish Acad. Sci. 33 (1985), 17-23.
• [15] K. Deimling, Multivalued Differential Equations, De Gruyter series in Nonlinear Analysis and Applications, Berlin 1992.
• [16] A. Gavioli, A viability result in the upper semicontinuous case, J. Convex Analysis 5-2 (1998).
• [17] L. Górniewicz, On the Solution Sets of Differential Inclusions, J. Math. Anal. Appl. 113 (1986), 235-244.
• [18] L. Górniewicz, Topological approach to differential inclusions, in Topological Methods in Differential Equations and Inclusions, ed. by A. Granas and M. Frigon, Kluwer Academic Publishers, Dordrecht-Boston-London 1995.
• [19] L. Górniewicz, Homological methods in fixed point theory of multivalued mappings, Dissertationes Math. 129 (1976), 1-71.
• [20] S. Hu and N.S. Papageorgiou, On the topological regularity of the solution set of differential inclusions with constraints, J. Diff. Equat. 107 (1994), 280-289.
• [21] S. Hu and N.S. Papageorgiou, Delay differential inclusions with constraints, Proc. Amer. Math. Soc. 123 (7) (1995), 2141-2150.
• [22] M.D.P. Monteiro Marques, Differential Inclusions in Monsmooth Mechanical Problems, Shocks and Dry Friction, Birkhäuser Verlag 1993.
• [23] J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Diff. Equat. 26 (1977), 347-374.
• [24] S. Plaskacz, Periodic solutions of differential inclusions on compact subsets of R^n}HUK, J. Math. Anal. Appl. 148 (1990), 202-212. Boll. U.M.I. (7) 7-A (1993), 409-420.
• [25] R.T. Rockafellar, Clarke's tangent cones and the boundaries of closed sets in R^n}HUK, Nonlinear Analysis 3 (1) (1979), 145-154.
• [26] M. Valadier, Quelques problemes d'entraî nement unilatéral en dimension finie, Sém. d'Anal. Convexe Montpellier (1988), exposé n. 8.